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Loop Quantum Gravity and Recent Progress

Loop Quantum Gravity and Recent Progress. Yi Ling ( 凌 意） ITP, Chinese Academy of Sciences Dec.27, 2003. Loop Quantum Gravity and Recent Progress. Brief history of loop quantum gravity Ashtekar-Sen variables Spin networks Applications and recent progress

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Loop Quantum Gravity and Recent Progress

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  1. Loop Quantum Gravity and Recent Progress Yi Ling (凌 意） ITP, Chinese Academy of Sciences Dec.27, 2003

  2. Loop Quantum Gravity and Recent Progress • Brief history of loop quantum gravity • Ashtekar-Sen variables • Spin networks • Applications and recent progress • Isolated horizon and entropy of black holes • Loop quantum cosmology • Positive cosmological constant and Chern-Simons states

  3. Einstein’s Dream

  4. Quantum mechanics +special relativity Quantum field theory Electromagnetic interaction (QED) Weak interaction Strong interaction (QCD) Renormalizable • Quantum field theory +general relativity Quantum gravity Gravitational interaction Non-renormalizable

  5. Advices From Dirac • How then do they manage with these incorrect equation? These equations lead to infinities when one tries to solve them; These infinities ought not to be there. They remove them artificially… ------ The inadequacies of quantum filed theory.

  6. General Relativity +Quantum Mechanics

  7. General Relativity +Quantum Mechanics • 3+1 decomposition

  8. General Relativity +Quantum Mechanics • Wheeler-Dewitt equation

  9. Ashtekar-Sen Variables • Ashtekar-Sen variables a: SU(2) index

  10. Constraints • 3+1 decomposition

  11. SU(2) Diff(M) H ? Solutions to These Equations • Three steps

  12. Loop States • Holonomy • Multi-loop states

  13. Spin Networks • Spin networks j 1 j 2 v j 1 3

  14. Discreteness of Quantum Geometry • Microscopic version of space

  15. Discreteness of Quantum Geometry • Area spectrum j

  16. Dynamics • Causal spin networks and spin foams t 3 t 2 t 1

  17. Recent Progress in Loop Quantum Gravity • Isolated horizons and dynamical black holes • Quantum gravity with positive cosmological constant • The absence of singularity in loop quantum cosmology • Extending it to supergravity and M theory

  18. Isolated Horizons and Statistical Entropy of Black Holes • Bekenstein-Hawking entropy

  19. A Quick Review on Isolated Horizons • Motivations • Origin of black hole entropy • Physical laws of general black holes The zeroth and first law: Stationary black holes • (Quasi)local quantities on the horizon The mass, angular momentum and charges: Global concepts

  20. A Quick Review on Isolated Horizons • Weakly isolated horizons • SO(3) (non-rotating) • Axi-symmetry(rotating) • Distortion • Dynamical horizons

  21. Boundary Theory on Isolated Horizons • Self-dual action

  22. Boundary Theory on Isolated Horizons • Consequences of boundary conditions on horizon

  23. Boundary Theory on Isolated Horizons

  24. Boundary Theory on Isolated Horizons • Quantization

  25. Boundary Theory on Isolated Horizons • From quantum general relativity • From quantum Chern-Simons theory

  26. Boundary Theory on Isolated Horizons • Hilbert space

  27. Boundary Theory on Isolated Horizons • Topological quantum field theory

  28. Discrete Horizons From Quantum Geometry • The most probable distribution • The area of discrete horizon

  29. Counting the Number of Microstates of Quantum Gravity • The entropy of discrete horizon

  30. Fixing the Immirzi Parameter • Quasinormal modes of black holes • Bohr’s correspondence principle

  31. Fixing the Immirzi Parameter • Quantum GR • Loop quantization of N=1 supergravity

  32. Some Progress in Loop Quantum Cosmology • The absence of singularity in loop quantum cosmology Closed universe with k=1, Scale factor Originated from a big-bang

  33. Some Progress in Loop Quantum Cosmology Quantum Mechanically We would expect Thus, is a classical relation.

  34. Some Progress in Loop Quantum Cosmology Quantum geometry

  35. n

  36. Some Progress in Loop Quantum Cosmology • Positive cosmological and Chern-Simons states

  37. Some Progress in Loop Quantum Cosmology • Kodama state • Problem of time • Energy-momentum relations(Lorentz Violation)

  38. M theory Loop Quantum GR String theory D=11 Supergravity D=10 Supergravity D=4,N=1,2 Supergravity D=4,N=8 Supergravity Extend It to supergravity and M Theory

  39. Thank You

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